Pairs and pieces

Find all such pairs of positive integers (m,n), for which a rectangle with dimensions of m x n can be built from such pieces created from 6 squares marked as "O" (note that you can both rotate and flip the pieces):

Code:

O O
OOOO

(if it's not clear, it's a F-type shape)

OK. So we now that we can create a 3x4 rectangle by simply putting together this shape and the one rotated by 180^:

Code:

OOOO
O O

As we can create 3x4, we can also create 4a x 3a for a positive integer a. But what else? I'm kind of clueless...